LMFDB - Embedded newform 8043.2.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85383 q^{2} +1.00000 q^{3} +1.43669 q^{4} -2.52734 q^{5} -1.85383 q^{6} +1.00000 q^{7} +1.04428 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.85383 q^{2} +1.00000 q^{3} +1.43669 q^{4} -2.52734 q^{5} -1.85383 q^{6} +1.00000 q^{7} +1.04428 q^{8} +1.00000 q^{9} +4.68526 q^{10} -0.833303 q^{11} +1.43669 q^{12} -4.92043 q^{13} -1.85383 q^{14} -2.52734 q^{15} -4.80930 q^{16} -5.89388 q^{17} -1.85383 q^{18} +7.44535 q^{19} -3.63101 q^{20} +1.00000 q^{21} +1.54480 q^{22} -5.86533 q^{23} +1.04428 q^{24} +1.38745 q^{25} +9.12164 q^{26} +1.00000 q^{27} +1.43669 q^{28} +5.69224 q^{29} +4.68526 q^{30} +4.75118 q^{31} +6.82707 q^{32} -0.833303 q^{33} +10.9263 q^{34} -2.52734 q^{35} +1.43669 q^{36} +6.55142 q^{37} -13.8024 q^{38} -4.92043 q^{39} -2.63926 q^{40} -5.95202 q^{41} -1.85383 q^{42} +5.78250 q^{43} -1.19720 q^{44} -2.52734 q^{45} +10.8733 q^{46} -2.42044 q^{47} -4.80930 q^{48} +1.00000 q^{49} -2.57210 q^{50} -5.89388 q^{51} -7.06913 q^{52} +8.29344 q^{53} -1.85383 q^{54} +2.10604 q^{55} +1.04428 q^{56} +7.44535 q^{57} -10.5525 q^{58} +10.7475 q^{59} -3.63101 q^{60} -0.0392400 q^{61} -8.80789 q^{62} +1.00000 q^{63} -3.03763 q^{64} +12.4356 q^{65} +1.54480 q^{66} -11.3891 q^{67} -8.46769 q^{68} -5.86533 q^{69} +4.68526 q^{70} -8.05016 q^{71} +1.04428 q^{72} +5.31904 q^{73} -12.1452 q^{74} +1.38745 q^{75} +10.6967 q^{76} -0.833303 q^{77} +9.12164 q^{78} +15.9023 q^{79} +12.1547 q^{80} +1.00000 q^{81} +11.0340 q^{82} +10.0852 q^{83} +1.43669 q^{84} +14.8959 q^{85} -10.7198 q^{86} +5.69224 q^{87} -0.870202 q^{88} -0.933448 q^{89} +4.68526 q^{90} -4.92043 q^{91} -8.42666 q^{92} +4.75118 q^{93} +4.48709 q^{94} -18.8170 q^{95} +6.82707 q^{96} -11.4662 q^{97} -1.85383 q^{98} -0.833303 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9} - 14 q^{10} - 29 q^{11} + 33 q^{12} - 40 q^{13} - 9 q^{14} - 27 q^{15} + 23 q^{16} - 46 q^{17} - 9 q^{18} + 17 q^{19} - 53 q^{20} + 40 q^{21} - 15 q^{22} - 62 q^{23} - 18 q^{24} + 35 q^{25} - 29 q^{26} + 40 q^{27} + 33 q^{28} - 47 q^{29} - 14 q^{30} + q^{31} - 45 q^{32} - 29 q^{33} + 9 q^{34} - 27 q^{35} + 33 q^{36} - 49 q^{37} - 52 q^{38} - 40 q^{39} - 12 q^{40} - 49 q^{41} - 9 q^{42} - 45 q^{43} - 68 q^{44} - 27 q^{45} - 36 q^{46} - 88 q^{47} + 23 q^{48} + 40 q^{49} - 32 q^{50} - 46 q^{51} - 34 q^{52} - 96 q^{53} - 9 q^{54} + 26 q^{55} - 18 q^{56} + 17 q^{57} + 12 q^{58} - 45 q^{59} - 53 q^{60} - 23 q^{61} - 15 q^{62} + 40 q^{63} + 50 q^{64} - 32 q^{65} - 15 q^{66} - 31 q^{67} - 76 q^{68} - 62 q^{69} - 14 q^{70} - 89 q^{71} - 18 q^{72} + 4 q^{73} + 10 q^{74} + 35 q^{75} + 51 q^{76} - 29 q^{77} - 29 q^{78} - 44 q^{79} - 53 q^{80} + 40 q^{81} - 15 q^{82} - 60 q^{83} + 33 q^{84} - 24 q^{85} - 9 q^{86} - 47 q^{87} - 64 q^{88} - 39 q^{89} - 14 q^{90} - 40 q^{91} - 80 q^{92} + q^{93} + 51 q^{94} - 71 q^{95} - 45 q^{96} - 21 q^{97} - 9 q^{98} - 29 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9 - 14 * q^10 - 29 * q^11 + 33 * q^12 - 40 * q^13 - 9 * q^14 - 27 * q^15 + 23 * q^16 - 46 * q^17 - 9 * q^18 + 17 * q^19 - 53 * q^20 + 40 * q^21 - 15 * q^22 - 62 * q^23 - 18 * q^24 + 35 * q^25 - 29 * q^26 + 40 * q^27 + 33 * q^28 - 47 * q^29 - 14 * q^30 + q^31 - 45 * q^32 - 29 * q^33 + 9 * q^34 - 27 * q^35 + 33 * q^36 - 49 * q^37 - 52 * q^38 - 40 * q^39 - 12 * q^40 - 49 * q^41 - 9 * q^42 - 45 * q^43 - 68 * q^44 - 27 * q^45 - 36 * q^46 - 88 * q^47 + 23 * q^48 + 40 * q^49 - 32 * q^50 - 46 * q^51 - 34 * q^52 - 96 * q^53 - 9 * q^54 + 26 * q^55 - 18 * q^56 + 17 * q^57 + 12 * q^58 - 45 * q^59 - 53 * q^60 - 23 * q^61 - 15 * q^62 + 40 * q^63 + 50 * q^64 - 32 * q^65 - 15 * q^66 - 31 * q^67 - 76 * q^68 - 62 * q^69 - 14 * q^70 - 89 * q^71 - 18 * q^72 + 4 * q^73 + 10 * q^74 + 35 * q^75 + 51 * q^76 - 29 * q^77 - 29 * q^78 - 44 * q^79 - 53 * q^80 + 40 * q^81 - 15 * q^82 - 60 * q^83 + 33 * q^84 - 24 * q^85 - 9 * q^86 - 47 * q^87 - 64 * q^88 - 39 * q^89 - 14 * q^90 - 40 * q^91 - 80 * q^92 + q^93 + 51 * q^94 - 71 * q^95 - 45 * q^96 - 21 * q^97 - 9 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.85383	−1.31086	−0.655428	−	0.755257i	$-0.727512\pi$
$2$	−1.85383	−1.31086	−0.655428	+	0.755257i	$0.727512\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.43669	0.718345
$5$	−2.52734	−1.13026	−0.565131	−	0.825001i	$-0.691174\pi$
$5$	−2.52734	−1.13026	−0.565131	+	0.825001i	$0.691174\pi$
$6$	−1.85383	−0.756823
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.04428	0.369209
$9$	1.00000	0.333333
$10$	4.68526	1.48161
$11$	−0.833303	−0.251250	−0.125625	−	0.992078i	$-0.540094\pi$
$11$	−0.833303	−0.251250	−0.125625	+	0.992078i	$0.540094\pi$
$12$	1.43669	0.414737
$13$	−4.92043	−1.36468	−0.682340	−	0.731035i	$-0.739038\pi$
$13$	−4.92043	−1.36468	−0.682340	+	0.731035i	$0.739038\pi$
$14$	−1.85383	−0.495457
$15$	−2.52734	−0.652557
$16$	−4.80930	−1.20233
$17$	−5.89388	−1.42948	−0.714738	−	0.699392i	$-0.753454\pi$
$17$	−5.89388	−1.42948	−0.714738	+	0.699392i	$0.753454\pi$
$18$	−1.85383	−0.436952
$19$	7.44535	1.70808	0.854041	−	0.520206i	$-0.174145\pi$
$19$	7.44535	1.70808	0.854041	+	0.520206i	$0.174145\pi$
$20$	−3.63101	−0.811918
$21$	1.00000	0.218218
$22$	1.54480	0.329353
$23$	−5.86533	−1.22301	−0.611503	−	0.791242i	$-0.709435\pi$
$23$	−5.86533	−1.22301	−0.611503	+	0.791242i	$0.709435\pi$
$24$	1.04428	0.213163
$25$	1.38745	0.277491
$26$	9.12164	1.78890
$27$	1.00000	0.192450
$28$	1.43669	0.271509
$29$	5.69224	1.05702	0.528511	−	0.848926i	$-0.322750\pi$
$29$	5.69224	1.05702	0.528511	+	0.848926i	$0.322750\pi$
$30$	4.68526	0.855408
$31$	4.75118	0.853338	0.426669	−	0.904408i	$-0.359687\pi$
$31$	4.75118	0.853338	0.426669	+	0.904408i	$0.359687\pi$
$32$	6.82707	1.20687
$33$	−0.833303	−0.145059
$34$	10.9263	1.87384
$35$	−2.52734	−0.427199
$36$	1.43669	0.239448
$37$	6.55142	1.07705	0.538523	−	0.842611i	$-0.318982\pi$
$37$	6.55142	1.07705	0.538523	+	0.842611i	$0.318982\pi$
$38$	−13.8024	−2.23905
$39$	−4.92043	−0.787899
$40$	−2.63926	−0.417303
$41$	−5.95202	−0.929549	−0.464774	−	0.885429i	$-0.653865\pi$
$41$	−5.95202	−0.929549	−0.464774	+	0.885429i	$0.653865\pi$
$42$	−1.85383	−0.286052
$43$	5.78250	0.881822	0.440911	−	0.897551i	$-0.354655\pi$
$43$	5.78250	0.881822	0.440911	+	0.897551i	$0.354655\pi$
$44$	−1.19720	−0.180484
$45$	−2.52734	−0.376754
$46$	10.8733	1.60319
$47$	−2.42044	−0.353057	−0.176529	−	0.984295i	$-0.556487\pi$
$47$	−2.42044	−0.353057	−0.176529	+	0.984295i	$0.556487\pi$
$48$	−4.80930	−0.694163
$49$	1.00000	0.142857
$50$	−2.57210	−0.363750
$51$	−5.89388	−0.825309
$52$	−7.06913	−0.980311
$53$	8.29344	1.13919	0.569596	−	0.821925i	$-0.307100\pi$
$53$	8.29344	1.13919	0.569596	+	0.821925i	$0.307100\pi$
$54$	−1.85383	−0.252274
$55$	2.10604	0.283978
$56$	1.04428	0.139548
$57$	7.44535	0.986161
$58$	−10.5525	−1.38560
$59$	10.7475	1.39921	0.699603	−	0.714531i	$-0.253360\pi$
$59$	10.7475	1.39921	0.699603	+	0.714531i	$0.253360\pi$
$60$	−3.63101	−0.468761
$61$	−0.0392400	−0.00502417	−0.00251209	−	0.999997i	$-0.500800\pi$
$61$	−0.0392400	−0.00502417	−0.00251209	+	0.999997i	$0.500800\pi$
$62$	−8.80789	−1.11860
$63$	1.00000	0.125988
$64$	−3.03763	−0.379704
$65$	12.4356	1.54245
$66$	1.54480	0.190152
$67$	−11.3891	−1.39140	−0.695701	−	0.718331i	$-0.744906\pi$
$67$	−11.3891	−1.39140	−0.695701	+	0.718331i	$0.744906\pi$
$68$	−8.46769	−1.02686
$69$	−5.86533	−0.706103
$70$	4.68526	0.559996
$71$	−8.05016	−0.955378	−0.477689	−	0.878529i	$-0.658525\pi$
$71$	−8.05016	−0.955378	−0.477689	+	0.878529i	$0.658525\pi$
$72$	1.04428	0.123070
$73$	5.31904	0.622546	0.311273	−	0.950321i	$-0.399245\pi$
$73$	5.31904	0.622546	0.311273	+	0.950321i	$0.399245\pi$
$74$	−12.1452	−1.41185
$75$	1.38745	0.160209
$76$	10.6967	1.22699
$77$	−0.833303	−0.0949636
$78$	9.12164	1.03282
$79$	15.9023	1.78915	0.894573	−	0.446922i	$-0.147480\pi$
$79$	15.9023	1.78915	0.894573	+	0.446922i	$0.147480\pi$
$80$	12.1547	1.35894
$81$	1.00000	0.111111
$82$	11.0340	1.21851
$83$	10.0852	1.10699	0.553497	−	0.832851i	$-0.313293\pi$
$83$	10.0852	1.10699	0.553497	+	0.832851i	$0.313293\pi$
$84$	1.43669	0.156756
$85$	14.8959	1.61568
$86$	−10.7198	−1.15594
$87$	5.69224	0.610272
$88$	−0.870202	−0.0927639
$89$	−0.933448	−0.0989452	−0.0494726	−	0.998775i	$-0.515754\pi$
$89$	−0.933448	−0.0989452	−0.0494726	+	0.998775i	$0.515754\pi$
$90$	4.68526	0.493870
$91$	−4.92043	−0.515801
$92$	−8.42666	−0.878540
$93$	4.75118	0.492675
$94$	4.48709	0.462808
$95$	−18.8170	−1.93058
$96$	6.82707	0.696785
$97$	−11.4662	−1.16421	−0.582106	−	0.813113i	$-0.697771\pi$
$97$	−11.4662	−1.16421	−0.582106	+	0.813113i	$0.697771\pi$
$98$	−1.85383	−0.187265
$99$	−0.833303	−0.0837501
$100$	1.99334	0.199334
$101$	0.288972	0.0287538	0.0143769	−	0.999897i	$-0.495424\pi$
$101$	0.288972	0.0287538	0.0143769	+	0.999897i	$0.495424\pi$
$102$	10.9263	1.08186
$103$	−4.54560	−0.447891	−0.223946	−	0.974602i	$-0.571894\pi$
$103$	−4.54560	−0.447891	−0.223946	+	0.974602i	$0.571894\pi$
$104$	−5.13831	−0.503853
$105$	−2.52734	−0.246643
$106$	−15.3746	−1.49332
$107$	−10.4822	−1.01335	−0.506676	−	0.862137i	$-0.669126\pi$
$107$	−10.4822	−1.01335	−0.506676	+	0.862137i	$0.669126\pi$
$108$	1.43669	0.138246
$109$	−7.17764	−0.687493	−0.343746	−	0.939063i	$-0.611696\pi$
$109$	−7.17764	−0.687493	−0.343746	+	0.939063i	$0.611696\pi$
$110$	−3.90424	−0.372255
$111$	6.55142	0.621833
$112$	−4.80930	−0.454436
$113$	−3.30712	−0.311108	−0.155554	−	0.987827i	$-0.549716\pi$
$113$	−3.30712	−0.311108	−0.155554	+	0.987827i	$0.549716\pi$
$114$	−13.8024	−1.29272
$115$	14.8237	1.38232
$116$	8.17799	0.759307
$117$	−4.92043	−0.454893
$118$	−19.9241	−1.83416
$119$	−5.89388	−0.540291
$120$	−2.63926	−0.240930
$121$	−10.3056	−0.936873
$122$	0.0727444	0.00658597
$123$	−5.95202	−0.536675
$124$	6.82598	0.612991
$125$	9.13014	0.816624
$126$	−1.85383	−0.165152
$127$	−18.0871	−1.60497	−0.802487	−	0.596669i	$-0.796491\pi$
$127$	−18.0871	−1.60497	−0.802487	+	0.596669i	$0.796491\pi$
$128$	−8.02288	−0.709129
$129$	5.78250	0.509120
$130$	−23.0535	−2.02192
$131$	18.5993	1.62503	0.812515	−	0.582940i	$-0.198098\pi$
$131$	18.5993	1.62503	0.812515	+	0.582940i	$0.198098\pi$
$132$	−1.19720	−0.104203
$133$	7.44535	0.645594
$134$	21.1135	1.82393
$135$	−2.52734	−0.217519
$136$	−6.15487	−0.527776
$137$	−10.8449	−0.926540	−0.463270	−	0.886217i	$-0.653324\pi$
$137$	−10.8449	−0.926540	−0.463270	+	0.886217i	$0.653324\pi$
$138$	10.8733	0.925600
$139$	1.85985	0.157750	0.0788751	−	0.996885i	$-0.474867\pi$
$139$	1.85985	0.157750	0.0788751	+	0.996885i	$0.474867\pi$
$140$	−3.63101	−0.306876
$141$	−2.42044	−0.203838
$142$	14.9236	1.25236
$143$	4.10020	0.342876
$144$	−4.80930	−0.400775
$145$	−14.3862	−1.19471
$146$	−9.86060	−0.816069
$147$	1.00000	0.0824786
$148$	9.41236	0.773691
$149$	−22.9074	−1.87665	−0.938326	−	0.345753i	$-0.887624\pi$
$149$	−22.9074	−1.87665	−0.938326	+	0.345753i	$0.887624\pi$
$150$	−2.57210	−0.210011
$151$	13.7415	1.11827	0.559134	−	0.829077i	$-0.311134\pi$
$151$	13.7415	1.11827	0.559134	+	0.829077i	$0.311134\pi$
$152$	7.77504	0.630639
$153$	−5.89388	−0.476492
$154$	1.54480	0.124484
$155$	−12.0079	−0.964494
$156$	−7.06913	−0.565983
$157$	3.42888	0.273654	0.136827	−	0.990595i	$-0.456309\pi$
$157$	3.42888	0.273654	0.136827	+	0.990595i	$0.456309\pi$
$158$	−29.4801	−2.34531
$159$	8.29344	0.657713
$160$	−17.2543	−1.36408
$161$	−5.86533	−0.462253
$162$	−1.85383	−0.145651
$163$	9.66186	0.756775	0.378387	−	0.925647i	$-0.376479\pi$
$163$	9.66186	0.756775	0.378387	+	0.925647i	$0.376479\pi$
$164$	−8.55120	−0.667737
$165$	2.10604	0.163955
$166$	−18.6962	−1.45111
$167$	−24.0559	−1.86150	−0.930751	−	0.365652i	$-0.880846\pi$
$167$	−24.0559	−1.86150	−0.930751	+	0.365652i	$0.880846\pi$
$168$	1.04428	0.0805681
$169$	11.2106	0.862353
$170$	−27.6144	−2.11793
$171$	7.44535	0.569360
$172$	8.30766	0.633453
$173$	6.66212	0.506512	0.253256	−	0.967399i	$-0.418499\pi$
$173$	6.66212	0.506512	0.253256	+	0.967399i	$0.418499\pi$
$174$	−10.5525	−0.799979
$175$	1.38745	0.104882
$176$	4.00760	0.302084
$177$	10.7475	0.807832
$178$	1.73045	0.129703
$179$	20.5220	1.53389	0.766943	−	0.641716i	$-0.221777\pi$
$179$	20.5220	1.53389	0.766943	+	0.641716i	$0.221777\pi$
$180$	−3.63101	−0.270639
$181$	−11.1376	−0.827849	−0.413925	−	0.910311i	$-0.635842\pi$
$181$	−11.1376	−0.827849	−0.413925	+	0.910311i	$0.635842\pi$
$182$	9.12164	0.676141
$183$	−0.0392400	−0.00290071
$184$	−6.12506	−0.451545
$185$	−16.5577	−1.21734
$186$	−8.80789	−0.645826
$187$	4.91139	0.359156
$188$	−3.47742	−0.253617
$189$	1.00000	0.0727393
$190$	34.8834	2.53071
$191$	14.0587	1.01725	0.508626	−	0.860988i	$-0.330154\pi$
$191$	14.0587	1.01725	0.508626	+	0.860988i	$0.330154\pi$
$192$	−3.03763	−0.219222
$193$	6.04385	0.435046	0.217523	−	0.976055i	$-0.430202\pi$
$193$	6.04385	0.435046	0.217523	+	0.976055i	$0.430202\pi$
$194$	21.2563	1.52612
$195$	12.4356	0.890531
$196$	1.43669	0.102621
$197$	−20.2982	−1.44619	−0.723094	−	0.690750i	$-0.757281\pi$
$197$	−20.2982	−1.44619	−0.723094	+	0.690750i	$0.757281\pi$
$198$	1.54480	0.109784
$199$	−3.96861	−0.281327	−0.140664	−	0.990057i	$-0.544924\pi$
$199$	−3.96861	−0.281327	−0.140664	+	0.990057i	$0.544924\pi$
$200$	1.44889	0.102452
$201$	−11.3891	−0.803326
$202$	−0.535705	−0.0376921
$203$	5.69224	0.399517
$204$	−8.46769	−0.592857
$205$	15.0428	1.05063
$206$	8.42678	0.587121
$207$	−5.86533	−0.407669
$208$	23.6638	1.64079
$209$	−6.20423	−0.429156
$210$	4.68526	0.323314
$211$	2.79179	0.192195	0.0960973	−	0.995372i	$-0.469364\pi$
$211$	2.79179	0.192195	0.0960973	+	0.995372i	$0.469364\pi$
$212$	11.9151	0.818333
$213$	−8.05016	−0.551588
$214$	19.4322	1.32836
$215$	−14.6143	−0.996690
$216$	1.04428	0.0710543
$217$	4.75118	0.322531
$218$	13.3061	0.901205
$219$	5.31904	0.359427
$220$	3.02573	0.203994
$221$	29.0004	1.95078
$222$	−12.1452	−0.815134
$223$	3.05324	0.204460	0.102230	−	0.994761i	$-0.467402\pi$
$223$	3.05324	0.204460	0.102230	+	0.994761i	$0.467402\pi$
$224$	6.82707	0.456153
$225$	1.38745	0.0924969
$226$	6.13084	0.407817
$227$	1.59951	0.106163	0.0530815	−	0.998590i	$-0.483096\pi$
$227$	1.59951	0.106163	0.0530815	+	0.998590i	$0.483096\pi$
$228$	10.6967	0.708404
$229$	24.7780	1.63738	0.818688	−	0.574239i	$-0.194702\pi$
$229$	24.7780	1.63738	0.818688	+	0.574239i	$0.194702\pi$
$230$	−27.4806	−1.81202
$231$	−0.833303	−0.0548273
$232$	5.94430	0.390262
$233$	−18.0402	−1.18185	−0.590926	−	0.806726i	$-0.701237\pi$
$233$	−18.0402	−1.18185	−0.590926	+	0.806726i	$0.701237\pi$
$234$	9.12164	0.596300
$235$	6.11728	0.399047
$236$	15.4408	1.00511
$237$	15.9023	1.03296
$238$	10.9263	0.708245
$239$	12.5370	0.810953	0.405476	−	0.914106i	$-0.367106\pi$
$239$	12.5370	0.810953	0.405476	+	0.914106i	$0.367106\pi$
$240$	12.1547	0.784585
$241$	23.1737	1.49275	0.746375	−	0.665526i	$-0.231793\pi$
$241$	23.1737	1.49275	0.746375	+	0.665526i	$0.231793\pi$
$242$	19.1049	1.22811
$243$	1.00000	0.0641500
$244$	−0.0563758	−0.00360909
$245$	−2.52734	−0.161466
$246$	11.0340	0.703504
$247$	−36.6343	−2.33099
$248$	4.96157	0.315060
$249$	10.0852	0.639123
$250$	−16.9257	−1.07048
$251$	1.79502	0.113301	0.0566503	−	0.998394i	$-0.481958\pi$
$251$	1.79502	0.113301	0.0566503	+	0.998394i	$0.481958\pi$
$252$	1.43669	0.0905030
$253$	4.88759	0.307280
$254$	33.5305	2.10389
$255$	14.8959	0.932815
$256$	20.9483	1.30927
$257$	−11.9796	−0.747264	−0.373632	−	0.927577i	$-0.621888\pi$
$257$	−11.9796	−0.747264	−0.373632	+	0.927577i	$0.621888\pi$
$258$	−10.7198	−0.667384
$259$	6.55142	0.407085
$260$	17.8661	1.10801
$261$	5.69224	0.352341
$262$	−34.4800	−2.13018
$263$	−20.6209	−1.27154	−0.635769	−	0.771879i	$-0.719317\pi$
$263$	−20.6209	−1.27154	−0.635769	+	0.771879i	$0.719317\pi$
$264$	−0.870202	−0.0535572
$265$	−20.9604	−1.28758
$266$	−13.8024	−0.846281
$267$	−0.933448	−0.0571261
$268$	−16.3626	−0.999507
$269$	−17.6428	−1.07570	−0.537849	−	0.843041i	$-0.680763\pi$
$269$	−17.6428	−1.07570	−0.537849	+	0.843041i	$0.680763\pi$
$270$	4.68526	0.285136
$271$	−29.4105	−1.78656	−0.893279	−	0.449502i	$-0.851601\pi$
$271$	−29.4105	−1.78656	−0.893279	+	0.449502i	$0.851601\pi$
$272$	28.3455	1.71870
$273$	−4.92043	−0.297798
$274$	20.1046	1.21456
$275$	−1.15617	−0.0697196
$276$	−8.42666	−0.507225
$277$	18.9728	1.13997	0.569983	−	0.821657i	$-0.306950\pi$
$277$	18.9728	1.13997	0.569983	+	0.821657i	$0.306950\pi$
$278$	−3.44785	−0.206788
$279$	4.75118	0.284446
$280$	−2.63926	−0.157726
$281$	−4.72501	−0.281871	−0.140935	−	0.990019i	$-0.545011\pi$
$281$	−4.72501	−0.281871	−0.140935	+	0.990019i	$0.545011\pi$
$282$	4.48709	0.267202
$283$	−3.99427	−0.237435	−0.118717	−	0.992928i	$-0.537878\pi$
$283$	−3.99427	−0.237435	−0.118717	+	0.992928i	$0.537878\pi$
$284$	−11.5656	−0.686291
$285$	−18.8170	−1.11462
$286$	−7.60108	−0.449462
$287$	−5.95202	−0.351336
$288$	6.82707	0.402289
$289$	17.7379	1.04340
$290$	26.6696	1.56610
$291$	−11.4662	−0.672158
$292$	7.64181	0.447203
$293$	−9.87371	−0.576828	−0.288414	−	0.957506i	$-0.593128\pi$
$293$	−9.87371	−0.576828	−0.288414	+	0.957506i	$0.593128\pi$
$294$	−1.85383	−0.108118
$295$	−27.1626	−1.58147
$296$	6.84152	0.397656
$297$	−0.833303	−0.0483531
$298$	42.4665	2.46002
$299$	28.8599	1.66901
$300$	1.99334	0.115086
$301$	5.78250	0.333298
$302$	−25.4744	−1.46589
$303$	0.288972	0.0166010
$304$	−35.8070	−2.05367
$305$	0.0991730	0.00567863
$306$	10.9263	0.624613
$307$	−31.0932	−1.77458	−0.887292	−	0.461207i	$-0.847416\pi$
$307$	−31.0932	−1.77458	−0.887292	+	0.461207i	$0.847416\pi$
$308$	−1.19720	−0.0682167
$309$	−4.54560	−0.258590
$310$	22.2605	1.26431
$311$	−16.8605	−0.956070	−0.478035	−	0.878341i	$-0.658651\pi$
$311$	−16.8605	−0.956070	−0.478035	+	0.878341i	$0.658651\pi$
$312$	−5.13831	−0.290899
$313$	30.2865	1.71189	0.855946	−	0.517065i	$-0.172975\pi$
$313$	30.2865	1.71189	0.855946	+	0.517065i	$0.172975\pi$
$314$	−6.35657	−0.358722
$315$	−2.52734	−0.142400
$316$	22.8466	1.28522
$317$	−5.43106	−0.305039	−0.152519	−	0.988300i	$-0.548739\pi$
$317$	−5.43106	−0.305039	−0.152519	+	0.988300i	$0.548739\pi$
$318$	−15.3746	−0.862167
$319$	−4.74336	−0.265577
$320$	7.67714	0.429165
$321$	−10.4822	−0.585059
$322$	10.8733	0.605947
$323$	−43.8821	−2.44166
$324$	1.43669	0.0798161
$325$	−6.82686	−0.378686
$326$	−17.9114	−0.992023
$327$	−7.17764	−0.396924
$328$	−6.21558	−0.343198
$329$	−2.42044	−0.133443
$330$	−3.90424	−0.214921
$331$	−13.4061	−0.736864	−0.368432	−	0.929655i	$-0.620105\pi$
$331$	−13.4061	−0.736864	−0.368432	+	0.929655i	$0.620105\pi$
$332$	14.4893	0.795204
$333$	6.55142	0.359016
$334$	44.5956	2.44016
$335$	28.7842	1.57265
$336$	−4.80930	−0.262369
$337$	−15.8690	−0.864437	−0.432218	−	0.901769i	$-0.642269\pi$
$337$	−15.8690	−0.864437	−0.432218	+	0.901769i	$0.642269\pi$
$338$	−20.7825	−1.13042
$339$	−3.30712	−0.179618
$340$	21.4007	1.16062
$341$	−3.95917	−0.214401
$342$	−13.8024	−0.746350
$343$	1.00000	0.0539949
$344$	6.03855	0.325577
$345$	14.8237	0.798081
$346$	−12.3505	−0.663964
$347$	3.34219	0.179418	0.0897091	−	0.995968i	$-0.471406\pi$
$347$	3.34219	0.179418	0.0897091	+	0.995968i	$0.471406\pi$
$348$	8.17799	0.438386
$349$	1.40951	0.0754492	0.0377246	−	0.999288i	$-0.487989\pi$
$349$	1.40951	0.0754492	0.0377246	+	0.999288i	$0.487989\pi$
$350$	−2.57210	−0.137485
$351$	−4.92043	−0.262633
$352$	−5.68902	−0.303226
$353$	1.61517	0.0859668	0.0429834	−	0.999076i	$-0.486314\pi$
$353$	1.61517	0.0859668	0.0429834	+	0.999076i	$0.486314\pi$
$354$	−19.9241	−1.05895
$355$	20.3455	1.07983
$356$	−1.34107	−0.0710768
$357$	−5.89388	−0.311937
$358$	−38.0443	−2.01070
$359$	−3.57960	−0.188924	−0.0944621	−	0.995528i	$-0.530113\pi$
$359$	−3.57960	−0.188924	−0.0944621	+	0.995528i	$0.530113\pi$
$360$	−2.63926	−0.139101
$361$	36.4333	1.91754
$362$	20.6472	1.08519
$363$	−10.3056	−0.540904
$364$	−7.06913	−0.370523
$365$	−13.4430	−0.703640
$366$	0.0727444	0.00380241
$367$	13.3581	0.697285	0.348642	−	0.937256i	$-0.386643\pi$
$367$	13.3581	0.697285	0.348642	+	0.937256i	$0.386643\pi$
$368$	28.2081	1.47045
$369$	−5.95202	−0.309850
$370$	30.6951	1.59576
$371$	8.29344	0.430574
$372$	6.82598	0.353910
$373$	33.9509	1.75791	0.878956	−	0.476903i	$-0.158241\pi$
$373$	33.9509	1.75791	0.878956	+	0.476903i	$0.158241\pi$
$374$	−9.10489	−0.470802
$375$	9.13014	0.471478
$376$	−2.52762	−0.130352
$377$	−28.0082	−1.44250
$378$	−1.85383	−0.0953508
$379$	−26.9633	−1.38501	−0.692505	−	0.721413i	$-0.743493\pi$
$379$	−26.9633	−1.38501	−0.692505	+	0.721413i	$0.743493\pi$
$380$	−27.0341	−1.38682
$381$	−18.0871	−0.926633
$382$	−26.0624	−1.33347
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−8.02288	−0.409416
$385$	2.10604	0.107334
$386$	−11.2043	−0.570283
$387$	5.78250	0.293941
$388$	−16.4733	−0.836306
$389$	−22.0387	−1.11740	−0.558702	−	0.829368i	$-0.688701\pi$
$389$	−22.0387	−1.11740	−0.558702	+	0.829368i	$0.688701\pi$
$390$	−23.0535	−1.16736
$391$	34.5696	1.74826
$392$	1.04428	0.0527442
$393$	18.5993	0.938212
$394$	37.6295	1.89574
$395$	−40.1905	−2.02220
$396$	−1.19720	−0.0601614
$397$	30.2802	1.51972	0.759861	−	0.650086i	$-0.225267\pi$
$397$	30.2802	1.51972	0.759861	+	0.650086i	$0.225267\pi$
$398$	7.35714	0.368780
$399$	7.44535	0.372734
$400$	−6.67268	−0.333634
$401$	−28.5807	−1.42725	−0.713626	−	0.700527i	$-0.752948\pi$
$401$	−28.5807	−1.42725	−0.713626	+	0.700527i	$0.752948\pi$
$402$	21.1135	1.05305
$403$	−23.3778	−1.16453
$404$	0.415163	0.0206551
$405$	−2.52734	−0.125585
$406$	−10.5525	−0.523709
$407$	−5.45931	−0.270608
$408$	−6.15487	−0.304712
$409$	32.6496	1.61442	0.807208	−	0.590266i	$-0.200977\pi$
$409$	32.6496	1.61442	0.807208	+	0.590266i	$0.200977\pi$
$410$	−27.8868	−1.37723
$411$	−10.8449	−0.534938
$412$	−6.53062	−0.321740
$413$	10.7475	0.528850
$414$	10.8733	0.534395
$415$	−25.4887	−1.25119
$416$	−33.5921	−1.64699
$417$	1.85985	0.0910772
$418$	11.5016	0.562562
$419$	−24.9537	−1.21907	−0.609535	−	0.792759i	$-0.708644\pi$
$419$	−24.9537	−1.21907	−0.609535	+	0.792759i	$0.708644\pi$
$420$	−3.63101	−0.177175
$421$	−19.4959	−0.950173	−0.475086	−	0.879939i	$-0.657583\pi$
$421$	−19.4959	−0.950173	−0.475086	+	0.879939i	$0.657583\pi$
$422$	−5.17550	−0.251940
$423$	−2.42044	−0.117686
$424$	8.66069	0.420600
$425$	−8.17749	−0.396666
$426$	14.9236	0.723052
$427$	−0.0392400	−0.00189896
$428$	−15.0597	−0.727936
$429$	4.10020	0.197960
$430$	27.0925	1.30652
$431$	−32.5835	−1.56949	−0.784746	−	0.619818i	$-0.787207\pi$
$431$	−32.5835	−1.56949	−0.784746	+	0.619818i	$0.787207\pi$
$432$	−4.80930	−0.231388
$433$	3.09718	0.148841	0.0744204	−	0.997227i	$-0.476289\pi$
$433$	3.09718	0.148841	0.0744204	+	0.997227i	$0.476289\pi$
$434$	−8.80789	−0.422792
$435$	−14.3862	−0.689767
$436$	−10.3120	−0.493857
$437$	−43.6695	−2.08899
$438$	−9.86060	−0.471158
$439$	−32.8510	−1.56789	−0.783947	−	0.620828i	$-0.786796\pi$
$439$	−32.8510	−1.56789	−0.783947	+	0.620828i	$0.786796\pi$
$440$	2.19930	0.104847
$441$	1.00000	0.0476190
$442$	−53.7619	−2.55719
$443$	−25.7922	−1.22543	−0.612713	−	0.790305i	$-0.709922\pi$
$443$	−25.7922	−1.22543	−0.612713	+	0.790305i	$0.709922\pi$
$444$	9.41236	0.446691
$445$	2.35914	0.111834
$446$	−5.66018	−0.268017
$447$	−22.9074	−1.08349
$448$	−3.03763	−0.143515
$449$	26.6809	1.25915	0.629575	−	0.776940i	$-0.283229\pi$
$449$	26.6809	1.25915	0.629575	+	0.776940i	$0.283229\pi$
$450$	−2.57210	−0.121250
$451$	4.95983	0.233549
$452$	−4.75130	−0.223483
$453$	13.7415	0.645632
$454$	−2.96522	−0.139164
$455$	12.4356	0.582990
$456$	7.77504	0.364100
$457$	−4.67606	−0.218737	−0.109369	−	0.994001i	$-0.534883\pi$
$457$	−4.67606	−0.218737	−0.109369	+	0.994001i	$0.534883\pi$
$458$	−45.9342	−2.14636
$459$	−5.89388	−0.275103
$460$	21.2971	0.992980
$461$	1.38664	0.0645822	0.0322911	−	0.999479i	$-0.489720\pi$
$461$	1.38664	0.0645822	0.0322911	+	0.999479i	$0.489720\pi$
$462$	1.54480	0.0718707
$463$	−7.74841	−0.360099	−0.180050	−	0.983658i	$-0.557626\pi$
$463$	−7.74841	−0.360099	−0.180050	+	0.983658i	$0.557626\pi$
$464$	−27.3757	−1.27088
$465$	−12.0079	−0.556851
$466$	33.4434	1.54924
$467$	8.08111	0.373949	0.186974	−	0.982365i	$-0.440132\pi$
$467$	8.08111	0.373949	0.186974	+	0.982365i	$0.440132\pi$
$468$	−7.06913	−0.326770
$469$	−11.3891	−0.525901
$470$	−11.3404	−0.523094
$471$	3.42888	0.157994
$472$	11.2234	0.516600
$473$	−4.81857	−0.221558
$474$	−29.4801	−1.35407
$475$	10.3301	0.473977
$476$	−8.46769	−0.388116
$477$	8.29344	0.379731
$478$	−23.2415	−1.06304
$479$	−24.3507	−1.11261	−0.556306	−	0.830977i	$-0.687782\pi$
$479$	−24.3507	−1.11261	−0.556306	+	0.830977i	$0.687782\pi$
$480$	−17.2543	−0.787549
$481$	−32.2358	−1.46982
$482$	−42.9601	−1.95678
$483$	−5.86533	−0.266882
$484$	−14.8060	−0.672998
$485$	28.9789	1.31586
$486$	−1.85383	−0.0840915
$487$	−17.9462	−0.813218	−0.406609	−	0.913602i	$-0.633289\pi$
$487$	−17.9462	−0.813218	−0.406609	+	0.913602i	$0.633289\pi$
$488$	−0.0409776	−0.00185497
$489$	9.66186	0.436924
$490$	4.68526	0.211659
$491$	−23.2252	−1.04814	−0.524070	−	0.851675i	$-0.675587\pi$
$491$	−23.2252	−1.04814	−0.524070	+	0.851675i	$0.675587\pi$
$492$	−8.55120	−0.385518
$493$	−33.5494	−1.51099
$494$	67.9138	3.05559
$495$	2.10604	0.0946594
$496$	−22.8499	−1.02599
$497$	−8.05016	−0.361099
$498$	−18.6962	−0.837799
$499$	7.97370	0.356952	0.178476	−	0.983944i	$-0.442883\pi$
$499$	7.97370	0.356952	0.178476	+	0.983944i	$0.442883\pi$
$500$	13.1172	0.586618
$501$	−24.0559	−1.07474
$502$	−3.32766	−0.148521
$503$	−5.04438	−0.224918	−0.112459	−	0.993656i	$-0.535873\pi$
$503$	−5.04438	−0.224918	−0.112459	+	0.993656i	$0.535873\pi$
$504$	1.04428	0.0465160
$505$	−0.730330	−0.0324993
$506$	−9.06078	−0.402801
$507$	11.2106	0.497880
$508$	−25.9856	−1.15293
$509$	41.1515	1.82401	0.912005	−	0.410179i	$-0.134534\pi$
$509$	41.1515	1.82401	0.912005	+	0.410179i	$0.134534\pi$
$510$	−27.6144	−1.22279
$511$	5.31904	0.235300
$512$	−22.7889	−1.00714
$513$	7.44535	0.328720
$514$	22.2081	0.979557
$515$	11.4883	0.506234
$516$	8.30766	0.365724
$517$	2.01696	0.0887057
$518$	−12.1452	−0.533631
$519$	6.66212	0.292435
$520$	12.9863	0.569485
$521$	−5.36311	−0.234962	−0.117481	−	0.993075i	$-0.537482\pi$
$521$	−5.36311	−0.234962	−0.117481	+	0.993075i	$0.537482\pi$
$522$	−10.5525	−0.461868
$523$	13.1860	0.576582	0.288291	−	0.957543i	$-0.406913\pi$
$523$	13.1860	0.576582	0.288291	+	0.957543i	$0.406913\pi$
$524$	26.7215	1.16733
$525$	1.38745	0.0605534
$526$	38.2276	1.66680
$527$	−28.0029	−1.21983
$528$	4.00760	0.174409
$529$	11.4021	0.495744
$530$	38.8570	1.68784
$531$	10.7475	0.466402
$532$	10.6967	0.463759
$533$	29.2865	1.26854
$534$	1.73045	0.0748841
$535$	26.4921	1.14535
$536$	−11.8934	−0.513719
$537$	20.5220	0.885589
$538$	32.7067	1.41009
$539$	−0.833303	−0.0358929
$540$	−3.63101	−0.156254
$541$	−1.00688	−0.0432891	−0.0216445	−	0.999766i	$-0.506890\pi$
$541$	−1.00688	−0.0432891	−0.0216445	+	0.999766i	$0.506890\pi$
$542$	54.5220	2.34192
$543$	−11.1376	−0.477959
$544$	−40.2380	−1.72519
$545$	18.1403	0.777047
$546$	9.12164	0.390370
$547$	−38.8873	−1.66270	−0.831349	−	0.555750i	$-0.812431\pi$
$547$	−38.8873	−1.66270	−0.831349	+	0.555750i	$0.812431\pi$
$548$	−15.5807	−0.665576
$549$	−0.0392400	−0.00167472
$550$	2.14334	0.0913923
$551$	42.3807	1.80548
$552$	−6.12506	−0.260700
$553$	15.9023	0.676234
$554$	−35.1724	−1.49433
$555$	−16.5577	−0.702834
$556$	2.67203	0.113319
$557$	−1.83364	−0.0776939	−0.0388469	−	0.999245i	$-0.512368\pi$
$557$	−1.83364	−0.0776939	−0.0388469	+	0.999245i	$0.512368\pi$
$558$	−8.80789	−0.372868
$559$	−28.4523	−1.20341
$560$	12.1547	0.513632
$561$	4.91139	0.207359
$562$	8.75938	0.369492
$563$	−8.26305	−0.348246	−0.174123	−	0.984724i	$-0.555709\pi$
$563$	−8.26305	−0.348246	−0.174123	+	0.984724i	$0.555709\pi$
$564$	−3.47742	−0.146426
$565$	8.35822	0.351633
$566$	7.40470	0.311243
$567$	1.00000	0.0419961
$568$	−8.40663	−0.352734
$569$	14.9016	0.624707	0.312354	−	0.949966i	$-0.398883\pi$
$569$	14.9016	0.624707	0.312354	+	0.949966i	$0.398883\pi$
$570$	34.8834	1.46111
$571$	30.5556	1.27871	0.639355	−	0.768911i	$-0.279201\pi$
$571$	30.5556	1.27871	0.639355	+	0.768911i	$0.279201\pi$
$572$	5.89072	0.246303
$573$	14.0587	0.587310
$574$	11.0340	0.460552
$575$	−8.13787	−0.339373
$576$	−3.03763	−0.126568
$577$	−16.1128	−0.670783	−0.335391	−	0.942079i	$-0.608869\pi$
$577$	−16.1128	−0.670783	−0.335391	+	0.942079i	$0.608869\pi$
$578$	−32.8830	−1.36775
$579$	6.04385	0.251174
$580$	−20.6686	−0.858215
$581$	10.0852	0.418404
$582$	21.2563	0.881103
$583$	−6.91095	−0.286222
$584$	5.55457	0.229850
$585$	12.4356	0.514148
$586$	18.3042	0.756139
$587$	−16.0602	−0.662874	−0.331437	−	0.943477i	$-0.607533\pi$
$587$	−16.0602	−0.662874	−0.331437	+	0.943477i	$0.607533\pi$
$588$	1.43669	0.0592481
$589$	35.3742	1.45757
$590$	50.3549	2.07308
$591$	−20.2982	−0.834957
$592$	−31.5078	−1.29496
$593$	22.9272	0.941508	0.470754	−	0.882265i	$-0.343982\pi$
$593$	22.9272	0.941508	0.470754	+	0.882265i	$0.343982\pi$
$594$	1.54480	0.0633840
$595$	14.8959	0.610671
$596$	−32.9109	−1.34808
$597$	−3.96861	−0.162424
$598$	−53.5014	−2.18784
$599$	−7.42427	−0.303347	−0.151674	−	0.988431i	$-0.548466\pi$
$599$	−7.42427	−0.303347	−0.151674	+	0.988431i	$0.548466\pi$
$600$	1.44889	0.0591507
$601$	−26.7654	−1.09179	−0.545893	−	0.837855i	$-0.683809\pi$
$601$	−26.7654	−1.09179	−0.545893	+	0.837855i	$0.683809\pi$
$602$	−10.7198	−0.436905
$603$	−11.3891	−0.463801
$604$	19.7423	0.803302
$605$	26.0458	1.05891
$606$	−0.535705	−0.0217615
$607$	−20.0137	−0.812330	−0.406165	−	0.913800i	$-0.633134\pi$
$607$	−20.0137	−0.812330	−0.406165	+	0.913800i	$0.633134\pi$
$608$	50.8300	2.06143
$609$	5.69224	0.230661
$610$	−0.183850	−0.00744387
$611$	11.9096	0.481811
$612$	−8.46769	−0.342286
$613$	−46.4969	−1.87799	−0.938997	−	0.343926i	$-0.888243\pi$
$613$	−46.4969	−1.87799	−0.938997	+	0.343926i	$0.888243\pi$
$614$	57.6416	2.32623
$615$	15.0428	0.606583
$616$	−0.870202	−0.0350614
$617$	−17.7149	−0.713175	−0.356587	−	0.934262i	$-0.616060\pi$
$617$	−17.7149	−0.713175	−0.356587	+	0.934262i	$0.616060\pi$
$618$	8.42678	0.338975
$619$	24.2164	0.973338	0.486669	−	0.873586i	$-0.338212\pi$
$619$	24.2164	0.973338	0.486669	+	0.873586i	$0.338212\pi$
$620$	−17.2516	−0.692840
$621$	−5.86533	−0.235368
$622$	31.2565	1.25327
$623$	−0.933448	−0.0373978
$624$	23.6638	0.947311
$625$	−30.0122	−1.20049
$626$	−56.1460	−2.24405
$627$	−6.20423	−0.247773
$628$	4.92624	0.196578
$629$	−38.6133	−1.53961
$630$	4.68526	0.186665
$631$	−23.8612	−0.949901	−0.474951	−	0.880012i	$-0.657534\pi$
$631$	−23.8612	−0.949901	−0.474951	+	0.880012i	$0.657534\pi$
$632$	16.6065	0.660569
$633$	2.79179	0.110964
$634$	10.0683	0.399862
$635$	45.7124	1.81404
$636$	11.9151	0.472465
$637$	−4.92043	−0.194954
$638$	8.79339	0.348133
$639$	−8.05016	−0.318459
$640$	20.2766	0.801501
$641$	−21.7154	−0.857705	−0.428853	−	0.903374i	$-0.641082\pi$
$641$	−21.7154	−0.857705	−0.428853	+	0.903374i	$0.641082\pi$
$642$	19.4322	0.766928
$643$	9.81426	0.387037	0.193518	−	0.981097i	$-0.438010\pi$
$643$	9.81426	0.387037	0.193518	+	0.981097i	$0.438010\pi$
$644$	−8.42666	−0.332057
$645$	−14.6143	−0.575439
$646$	81.3499	3.20067
$647$	26.3820	1.03718	0.518592	−	0.855022i	$-0.326456\pi$
$647$	26.3820	1.03718	0.518592	+	0.855022i	$0.326456\pi$
$648$	1.04428	0.0410232
$649$	−8.95593	−0.351551
$650$	12.6558	0.496403
$651$	4.75118	0.186214
$652$	13.8811	0.543626
$653$	35.0824	1.37288	0.686440	−	0.727186i	$-0.259172\pi$
$653$	35.0824	1.37288	0.686440	+	0.727186i	$0.259172\pi$
$654$	13.3061	0.520311
$655$	−47.0069	−1.83671
$656$	28.6250	1.11762
$657$	5.31904	0.207515
$658$	4.48709	0.174925
$659$	−8.63210	−0.336259	−0.168129	−	0.985765i	$-0.553773\pi$
$659$	−8.63210	−0.336259	−0.168129	+	0.985765i	$0.553773\pi$
$660$	3.02573	0.117776
$661$	−25.5426	−0.993492	−0.496746	−	0.867896i	$-0.665472\pi$
$661$	−25.5426	−0.993492	−0.496746	+	0.867896i	$0.665472\pi$
$662$	24.8526	0.965922
$663$	29.0004	1.12628
$664$	10.5318	0.408712
$665$	−18.8170	−0.729690
$666$	−12.1452	−0.470618
$667$	−33.3869	−1.29274
$668$	−34.5609	−1.33720
$669$	3.05324	0.118045
$670$	−53.3610	−2.06152
$671$	0.0326988	0.00126232
$672$	6.82707	0.263360
$673$	10.0611	0.387826	0.193913	−	0.981019i	$-0.437882\pi$
$673$	10.0611	0.387826	0.193913	+	0.981019i	$0.437882\pi$
$674$	29.4184	1.13315
$675$	1.38745	0.0534031
$676$	16.1061	0.619467
$677$	24.6884	0.948853	0.474426	−	0.880295i	$-0.342655\pi$
$677$	24.6884	0.948853	0.474426	+	0.880295i	$0.342655\pi$
$678$	6.13084	0.235453
$679$	−11.4662	−0.440031
$680$	15.5555	0.596525
$681$	1.59951	0.0612932
$682$	7.33964	0.281049
$683$	−13.0775	−0.500396	−0.250198	−	0.968195i	$-0.580496\pi$
$683$	−13.0775	−0.500396	−0.250198	+	0.968195i	$0.580496\pi$
$684$	10.6967	0.408997
$685$	27.4087	1.04723
$686$	−1.85383	−0.0707796
$687$	24.7780	0.945339
$688$	−27.8098	−1.06024
$689$	−40.8073	−1.55463
$690$	−27.4806	−1.04617
$691$	1.18587	0.0451125	0.0225563	−	0.999746i	$-0.492820\pi$
$691$	1.18587	0.0451125	0.0225563	+	0.999746i	$0.492820\pi$
$692$	9.57141	0.363850
$693$	−0.833303	−0.0316545
$694$	−6.19586	−0.235191
$695$	−4.70047	−0.178299
$696$	5.94430	0.225318
$697$	35.0805	1.32877
$698$	−2.61299	−0.0989031
$699$	−18.0402	−0.682342
$700$	1.99334	0.0753412
$701$	17.7565	0.670654	0.335327	−	0.942102i	$-0.391153\pi$
$701$	17.7565	0.670654	0.335327	+	0.942102i	$0.391153\pi$
$702$	9.12164	0.344274
$703$	48.7776	1.83968
$704$	2.53127	0.0954007
$705$	6.11728	0.230390
$706$	−2.99425	−0.112690
$707$	0.288972	0.0108679
$708$	15.4408	0.580302
$709$	−41.6172	−1.56297	−0.781484	−	0.623926i	$-0.785537\pi$
$709$	−41.6172	−1.56297	−0.781484	+	0.623926i	$0.785537\pi$
$710$	−37.7171	−1.41550
$711$	15.9023	0.596382
$712$	−0.974782	−0.0365315
$713$	−27.8673	−1.04364
$714$	10.9263	0.408905
$715$	−10.3626	−0.387540
$716$	29.4837	1.10186
$717$	12.5370	0.468204
$718$	6.63598	0.247653
$719$	32.3187	1.20529	0.602643	−	0.798011i	$-0.294114\pi$
$719$	32.3187	1.20529	0.602643	+	0.798011i	$0.294114\pi$
$720$	12.1547	0.452981
$721$	−4.54560	−0.169287
$722$	−67.5412	−2.51362
$723$	23.1737	0.861839
$724$	−16.0012	−0.594682
$725$	7.89772	0.293314
$726$	19.1049	0.709048
$727$	10.6044	0.393296	0.196648	−	0.980474i	$-0.436994\pi$
$727$	10.6044	0.393296	0.196648	+	0.980474i	$0.436994\pi$
$728$	−5.13831	−0.190438
$729$	1.00000	0.0370370
$730$	24.9211	0.922371
$731$	−34.0814	−1.26054
$732$	−0.0563758	−0.00208371
$733$	−50.6274	−1.86997	−0.934983	−	0.354692i	$-0.884586\pi$
$733$	−50.6274	−1.86997	−0.934983	+	0.354692i	$0.884586\pi$
$734$	−24.7636	−0.914040
$735$	−2.52734	−0.0932224
$736$	−40.0430	−1.47601
$737$	9.49058	0.349590
$738$	11.0340	0.406168
$739$	−24.6119	−0.905364	−0.452682	−	0.891672i	$-0.649533\pi$
$739$	−24.6119	−0.905364	−0.452682	+	0.891672i	$0.649533\pi$
$740$	−23.7882	−0.874473
$741$	−36.6343	−1.34580
$742$	−15.3746	−0.564421
$743$	−1.20389	−0.0441666	−0.0220833	−	0.999756i	$-0.507030\pi$
$743$	−1.20389	−0.0441666	−0.0220833	+	0.999756i	$0.507030\pi$
$744$	4.96157	0.181900
$745$	57.8949	2.12111
$746$	−62.9393	−2.30437
$747$	10.0852	0.368998
$748$	7.05614	0.257998
$749$	−10.4822	−0.383011
$750$	−16.9257	−0.618040
$751$	9.35423	0.341341	0.170670	−	0.985328i	$-0.445407\pi$
$751$	9.35423	0.341341	0.170670	+	0.985328i	$0.445407\pi$
$752$	11.6406	0.424490
$753$	1.79502	0.0654142
$754$	51.9226	1.89091
$755$	−34.7295	−1.26393
$756$	1.43669	0.0522519
$757$	−47.6811	−1.73300	−0.866499	−	0.499179i	$-0.833635\pi$
$757$	−47.6811	−1.73300	−0.866499	+	0.499179i	$0.833635\pi$
$758$	49.9854	1.81555
$759$	4.88759	0.177408
$760$	−19.6502	−0.712787
$761$	−48.8409	−1.77048	−0.885241	−	0.465133i	$-0.846006\pi$
$761$	−48.8409	−1.77048	−0.885241	+	0.465133i	$0.846006\pi$
$762$	33.5305	1.21468
$763$	−7.17764	−0.259848
$764$	20.1980	0.730738
$765$	14.8959	0.538561
$766$	1.85383	0.0669816
$767$	−52.8823	−1.90947
$768$	20.9483	0.755908
$769$	−13.4296	−0.484283	−0.242141	−	0.970241i	$-0.577850\pi$
$769$	−13.4296	−0.484283	−0.242141	+	0.970241i	$0.577850\pi$
$770$	−3.90424	−0.140699
$771$	−11.9796	−0.431433
$772$	8.68314	0.312513
$773$	34.1415	1.22798	0.613992	−	0.789312i	$-0.289563\pi$
$773$	34.1415	1.22798	0.613992	+	0.789312i	$0.289563\pi$
$774$	−10.7198	−0.385314
$775$	6.59204	0.236793
$776$	−11.9739	−0.429838
$777$	6.55142	0.235031
$778$	40.8560	1.46476
$779$	−44.3149	−1.58775
$780$	17.8661	0.639709
$781$	6.70822	0.240039
$782$	−64.0862	−2.29172
$783$	5.69224	0.203424
$784$	−4.80930	−0.171761
$785$	−8.66595	−0.309301
$786$	−34.4800	−1.22986
$787$	0.328956	0.0117260	0.00586301	−	0.999983i	$-0.498134\pi$
$787$	0.328956	0.0117260	0.00586301	+	0.999983i	$0.498134\pi$
$788$	−29.1622	−1.03886
$789$	−20.6209	−0.734123
$790$	74.5064	2.65082
$791$	−3.30712	−0.117588
$792$	−0.870202	−0.0309213
$793$	0.193078	0.00685639
$794$	−56.1344	−1.99214
$795$	−20.9604	−0.743387
$796$	−5.70167	−0.202090
$797$	−22.4237	−0.794288	−0.397144	−	0.917756i	$-0.629999\pi$
$797$	−22.4237	−0.794288	−0.397144	+	0.917756i	$0.629999\pi$
$798$	−13.8024	−0.488601
$799$	14.2658	0.504687
$800$	9.47224	0.334894
$801$	−0.933448	−0.0329817
$802$	52.9838	1.87092
$803$	−4.43237	−0.156415
$804$	−16.3626	−0.577066
$805$	14.8237	0.522466
$806$	43.3386	1.52654
$807$	−17.6428	−0.621054
$808$	0.301768	0.0106162
$809$	0.00299955	0.000105459 0	5.27293e−5	−	1.00000i	$-0.499983\pi$
$809$	0.00299955	0.000105459 0	5.27293e−5		1.00000i	$0.499983\pi$
$810$	4.68526	0.164623
$811$	−9.27984	−0.325859	−0.162930	−	0.986638i	$-0.552094\pi$
$811$	−9.27984	−0.325859	−0.162930	+	0.986638i	$0.552094\pi$
$812$	8.17799	0.286991
$813$	−29.4105	−1.03147
$814$	10.1206	0.354728
$815$	−24.4188	−0.855353
$816$	28.3455	0.992290
$817$	43.0527	1.50622
$818$	−60.5268	−2.11627
$819$	−4.92043	−0.171934
$820$	21.6118	0.754717
$821$	45.8425	1.59991	0.799957	−	0.600058i	$-0.204856\pi$
$821$	45.8425	1.59991	0.799957	+	0.600058i	$0.204856\pi$
$822$	20.1046	0.701227
$823$	−4.44464	−0.154931	−0.0774653	−	0.996995i	$-0.524683\pi$
$823$	−4.44464	−0.154931	−0.0774653	+	0.996995i	$0.524683\pi$
$824$	−4.74689	−0.165366
$825$	−1.15617	−0.0402526
$826$	−19.9241	−0.693247
$827$	41.0069	1.42595	0.712974	−	0.701190i	$-0.247348\pi$
$827$	41.0069	1.42595	0.712974	+	0.701190i	$0.247348\pi$
$828$	−8.42666	−0.292847
$829$	−19.3548	−0.672221	−0.336110	−	0.941823i	$-0.609112\pi$
$829$	−19.3548	−0.672221	−0.336110	+	0.941823i	$0.609112\pi$
$830$	47.2518	1.64013
$831$	18.9728	0.658160
$832$	14.9464	0.518175
$833$	−5.89388	−0.204211
$834$	−3.44785	−0.119389
$835$	60.7975	2.10398
$836$	−8.91356	−0.308282
$837$	4.75118	0.164225
$838$	46.2600	1.59803
$839$	0.230717	0.00796523	0.00398262	−	0.999992i	$-0.498732\pi$
$839$	0.230717	0.00796523	0.00398262	+	0.999992i	$0.498732\pi$
$840$	−2.63926	−0.0910630
$841$	3.40160	0.117297
$842$	36.1421	1.24554
$843$	−4.72501	−0.162738
$844$	4.01093	0.138062
$845$	−28.3330	−0.974684
$846$	4.48709	0.154269
$847$	−10.3056	−0.354105
$848$	−39.8857	−1.36968
$849$	−3.99427	−0.137083
$850$	15.1597	0.519973
$851$	−38.4262	−1.31723
$852$	−11.5656	−0.396230
$853$	25.1307	0.860457	0.430229	−	0.902720i	$-0.358433\pi$
$853$	25.1307	0.860457	0.430229	+	0.902720i	$0.358433\pi$
$854$	0.0727444	0.00248926
$855$	−18.8170	−0.643526
$856$	−10.9464	−0.374139
$857$	43.1902	1.47535	0.737675	−	0.675156i	$-0.235924\pi$
$857$	43.1902	1.47535	0.737675	+	0.675156i	$0.235924\pi$
$858$	−7.60108	−0.259497
$859$	37.1063	1.26605	0.633025	−	0.774131i	$-0.281813\pi$
$859$	37.1063	1.26605	0.633025	+	0.774131i	$0.281813\pi$
$860$	−20.9963	−0.715967
$861$	−5.95202	−0.202844
$862$	60.4043	2.05738
$863$	1.17134	0.0398730	0.0199365	−	0.999801i	$-0.493654\pi$
$863$	1.17134	0.0398730	0.0199365	+	0.999801i	$0.493654\pi$
$864$	6.82707	0.232262
$865$	−16.8375	−0.572491
$866$	−5.74164	−0.195109
$867$	17.7379	0.602410
$868$	6.82598	0.231689
$869$	−13.2514	−0.449523
$870$	26.6696	0.904186
$871$	56.0393	1.89882
$872$	−7.49547	−0.253829
$873$	−11.4662	−0.388071
$874$	80.9558	2.73837
$875$	9.13014	0.308655
$876$	7.64181	0.258193
$877$	−46.5861	−1.57310	−0.786551	−	0.617525i	$-0.788135\pi$
$877$	−46.5861	−1.57310	−0.786551	+	0.617525i	$0.788135\pi$
$878$	60.9002	2.05528
$879$	−9.87371	−0.333032
$880$	−10.1286	−0.341434
$881$	−3.93094	−0.132437	−0.0662184	−	0.997805i	$-0.521093\pi$
$881$	−3.93094	−0.132437	−0.0662184	+	0.997805i	$0.521093\pi$
$882$	−1.85383	−0.0624217
$883$	−35.5025	−1.19475	−0.597377	−	0.801960i	$-0.703791\pi$
$883$	−35.5025	−1.19475	−0.597377	+	0.801960i	$0.703791\pi$
$884$	41.6646	1.40133
$885$	−27.1626	−0.913062
$886$	47.8145	1.60636
$887$	−14.7634	−0.495707	−0.247854	−	0.968797i	$-0.579725\pi$
$887$	−14.7634	−0.495707	−0.247854	+	0.968797i	$0.579725\pi$
$888$	6.84152	0.229587
$889$	−18.0871	−0.606624
$890$	−4.37345	−0.146598
$891$	−0.833303	−0.0279167
$892$	4.38655	0.146873
$893$	−18.0210	−0.603051
$894$	42.4665	1.42029
$895$	−51.8661	−1.73369
$896$	−8.02288	−0.268026
$897$	28.8599	0.963605
$898$	−49.4619	−1.65056
$899$	27.0449	0.901997
$900$	1.99334	0.0664447
$901$	−48.8806	−1.62845
$902$	−9.19469	−0.306150
$903$	5.78250	0.192429
$904$	−3.45356	−0.114864
$905$	28.1485	0.935686
$906$	−25.4744	−0.846331
$907$	−19.9577	−0.662685	−0.331342	−	0.943511i	$-0.607502\pi$
$907$	−19.9577	−0.662685	−0.331342	+	0.943511i	$0.607502\pi$
$908$	2.29800	0.0762617
$909$	0.288972	0.00958459
$910$	−23.0535	−0.764216
$911$	−12.1629	−0.402974	−0.201487	−	0.979491i	$-0.564577\pi$
$911$	−12.1629	−0.402974	−0.201487	+	0.979491i	$0.564577\pi$
$912$	−35.8070	−1.18569
$913$	−8.40402	−0.278132
$914$	8.66863	0.286733
$915$	0.0991730	0.00327856
$916$	35.5983	1.17620
$917$	18.5993	0.614204
$918$	10.9263	0.360621
$919$	1.56071	0.0514830	0.0257415	−	0.999669i	$-0.491805\pi$
$919$	1.56071	0.0514830	0.0257415	+	0.999669i	$0.491805\pi$
$920$	15.4801	0.510364
$921$	−31.0932	−1.02456
$922$	−2.57060	−0.0846581
$923$	39.6102	1.30379
$924$	−1.19720	−0.0393849
$925$	9.08979	0.298870
$926$	14.3642	0.472038
$927$	−4.54560	−0.149297
$928$	38.8613	1.27569
$929$	−20.2263	−0.663604	−0.331802	−	0.943349i	$-0.607657\pi$
$929$	−20.2263	−0.663604	−0.331802	+	0.943349i	$0.607657\pi$
$930$	22.2605	0.729952
$931$	7.44535	0.244012
$932$	−25.9181	−0.848977
$933$	−16.8605	−0.551987
$934$	−14.9810	−0.490194
$935$	−12.4128	−0.405940
$936$	−5.13831	−0.167951
$937$	30.5462	0.997902	0.498951	−	0.866630i	$-0.333719\pi$
$937$	30.5462	0.997902	0.498951	+	0.866630i	$0.333719\pi$
$938$	21.1135	0.689380
$939$	30.2865	0.988362
$940$	8.78863	0.286654
$941$	4.52745	0.147591	0.0737954	−	0.997273i	$-0.476489\pi$
$941$	4.52745	0.147591	0.0737954	+	0.997273i	$0.476489\pi$
$942$	−6.35657	−0.207108
$943$	34.9105	1.13684
$944$	−51.6880	−1.68230
$945$	−2.52734	−0.0822144
$946$	8.93281	0.290431
$947$	24.3024	0.789721	0.394860	−	0.918741i	$-0.370793\pi$
$947$	24.3024	0.789721	0.394860	+	0.918741i	$0.370793\pi$
$948$	22.8466	0.742025
$949$	−26.1719	−0.849577
$950$	−19.1502	−0.621315
$951$	−5.43106	−0.176114
$952$	−6.15487	−0.199481
$953$	50.7439	1.64375	0.821877	−	0.569665i	$-0.192927\pi$
$953$	50.7439	1.64375	0.821877	+	0.569665i	$0.192927\pi$
$954$	−15.3746	−0.497773
$955$	−35.5311	−1.14976
$956$	18.0118	0.582544
$957$	−4.74336	−0.153331
$958$	45.1421	1.45848
$959$	−10.8449	−0.350199
$960$	7.67714	0.247779
$961$	−8.42627	−0.271815
$962$	59.7597	1.92673
$963$	−10.4822	−0.337784
$964$	33.2934	1.07231
$965$	−15.2749	−0.491715
$966$	10.8733	0.349844
$967$	−9.60190	−0.308776	−0.154388	−	0.988010i	$-0.549341\pi$
$967$	−9.60190	−0.308776	−0.154388	+	0.988010i	$0.549341\pi$
$968$	−10.7620	−0.345902
$969$	−43.8821	−1.40969
$970$	−53.7220	−1.72491
$971$	4.75493	0.152593	0.0762965	−	0.997085i	$-0.475690\pi$
$971$	4.75493	0.152593	0.0762965	+	0.997085i	$0.475690\pi$
$972$	1.43669	0.0460819
$973$	1.85985	0.0596240
$974$	33.2692	1.06601
$975$	−6.82686	−0.218634
$976$	0.188717	0.00604069
$977$	−27.8305	−0.890376	−0.445188	−	0.895437i	$-0.646863\pi$
$977$	−27.8305	−0.890376	−0.445188	+	0.895437i	$0.646863\pi$
$978$	−17.9114	−0.572745
$979$	0.777844	0.0248600
$980$	−3.63101	−0.115988
$981$	−7.17764	−0.229164
$982$	43.0557	1.37396
$983$	−49.0048	−1.56301	−0.781506	−	0.623898i	$-0.785548\pi$
$983$	−49.0048	−1.56301	−0.781506	+	0.623898i	$0.785548\pi$
$984$	−6.21558	−0.198145
$985$	51.3005	1.63457
$986$	62.1949	1.98069
$987$	−2.42044	−0.0770434
$988$	−52.6322	−1.67445
$989$	−33.9163	−1.07847
$990$	−3.90424	−0.124085
$991$	−1.20896	−0.0384039	−0.0192020	−	0.999816i	$-0.506113\pi$
$991$	−1.20896	−0.0384039	−0.0192020	+	0.999816i	$0.506113\pi$
$992$	32.4367	1.02986
$993$	−13.4061	−0.425428
$994$	14.9236	0.473349
$995$	10.0300	0.317974
$996$	14.4893	0.459111
$997$	−59.7491	−1.89227	−0.946137	−	0.323767i	$-0.895051\pi$
$997$	−59.7491	−1.89227	−0.946137	+	0.323767i	$0.895051\pi$
$998$	−14.7819	−0.467913
$999$	6.55142	0.207278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.n.1.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.n.1.9	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85383 q^{2} +1.00000 q^{3} +1.43669 q^{4} -2.52734 q^{5} -1.85383 q^{6} +1.00000 q^{7} +1.04428 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.85383 q^{2} +1.00000 q^{3} +1.43669 q^{4} -2.52734 q^{5} -1.85383 q^{6} +1.00000 q^{7} +1.04428 q^{8} +1.00000 q^{9} +4.68526 q^{10} -0.833303 q^{11} +1.43669 q^{12} -4.92043 q^{13} -1.85383 q^{14} -2.52734 q^{15} -4.80930 q^{16} -5.89388 q^{17} -1.85383 q^{18} +7.44535 q^{19} -3.63101 q^{20} +1.00000 q^{21} +1.54480 q^{22} -5.86533 q^{23} +1.04428 q^{24} +1.38745 q^{25} +9.12164 q^{26} +1.00000 q^{27} +1.43669 q^{28} +5.69224 q^{29} +4.68526 q^{30} +4.75118 q^{31} +6.82707 q^{32} -0.833303 q^{33} +10.9263 q^{34} -2.52734 q^{35} +1.43669 q^{36} +6.55142 q^{37} -13.8024 q^{38} -4.92043 q^{39} -2.63926 q^{40} -5.95202 q^{41} -1.85383 q^{42} +5.78250 q^{43} -1.19720 q^{44} -2.52734 q^{45} +10.8733 q^{46} -2.42044 q^{47} -4.80930 q^{48} +1.00000 q^{49} -2.57210 q^{50} -5.89388 q^{51} -7.06913 q^{52} +8.29344 q^{53} -1.85383 q^{54} +2.10604 q^{55} +1.04428 q^{56} +7.44535 q^{57} -10.5525 q^{58} +10.7475 q^{59} -3.63101 q^{60} -0.0392400 q^{61} -8.80789 q^{62} +1.00000 q^{63} -3.03763 q^{64} +12.4356 q^{65} +1.54480 q^{66} -11.3891 q^{67} -8.46769 q^{68} -5.86533 q^{69} +4.68526 q^{70} -8.05016 q^{71} +1.04428 q^{72} +5.31904 q^{73} -12.1452 q^{74} +1.38745 q^{75} +10.6967 q^{76} -0.833303 q^{77} +9.12164 q^{78} +15.9023 q^{79} +12.1547 q^{80} +1.00000 q^{81} +11.0340 q^{82} +10.0852 q^{83} +1.43669 q^{84} +14.8959 q^{85} -10.7198 q^{86} +5.69224 q^{87} -0.870202 q^{88} -0.933448 q^{89} +4.68526 q^{90} -4.92043 q^{91} -8.42666 q^{92} +4.75118 q^{93} +4.48709 q^{94} -18.8170 q^{95} +6.82707 q^{96} -11.4662 q^{97} -1.85383 q^{98} -0.833303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 9 q^{2} + 40 q^{3} + 33 q^{4} - 27 q^{5} - 9 q^{6} + 40 q^{7} - 18 q^{8} + 40 q^{9} - 14 q^{10} - 29 q^{11} + 33 q^{12} - 40 q^{13} - 9 q^{14} - 27 q^{15} + 23 q^{16} - 46 q^{17} - 9 q^{18} + 17 q^{19} - 53 q^{20} + 40 q^{21} - 15 q^{22} - 62 q^{23} - 18 q^{24} + 35 q^{25} - 29 q^{26} + 40 q^{27} + 33 q^{28} - 47 q^{29} - 14 q^{30} + q^{31} - 45 q^{32} - 29 q^{33} + 9 q^{34} - 27 q^{35} + 33 q^{36} - 49 q^{37} - 52 q^{38} - 40 q^{39} - 12 q^{40} - 49 q^{41} - 9 q^{42} - 45 q^{43} - 68 q^{44} - 27 q^{45} - 36 q^{46} - 88 q^{47} + 23 q^{48} + 40 q^{49} - 32 q^{50} - 46 q^{51} - 34 q^{52} - 96 q^{53} - 9 q^{54} + 26 q^{55} - 18 q^{56} + 17 q^{57} + 12 q^{58} - 45 q^{59} - 53 q^{60} - 23 q^{61} - 15 q^{62} + 40 q^{63} + 50 q^{64} - 32 q^{65} - 15 q^{66} - 31 q^{67} - 76 q^{68} - 62 q^{69} - 14 q^{70} - 89 q^{71} - 18 q^{72} + 4 q^{73} + 10 q^{74} + 35 q^{75} + 51 q^{76} - 29 q^{77} - 29 q^{78} - 44 q^{79} - 53 q^{80} + 40 q^{81} - 15 q^{82} - 60 q^{83} + 33 q^{84} - 24 q^{85} - 9 q^{86} - 47 q^{87} - 64 q^{88} - 39 q^{89} - 14 q^{90} - 40 q^{91} - 80 q^{92} + q^{93} + 51 q^{94} - 71 q^{95} - 45 q^{96} - 21 q^{97} - 9 q^{98} - 29 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 + 40 * q^3 + 33 * q^4 - 27 * q^5 - 9 * q^6 + 40 * q^7 - 18 * q^8 + 40 * q^9 - 14 * q^10 - 29 * q^11 + 33 * q^12 - 40 * q^13 - 9 * q^14 - 27 * q^15 + 23 * q^16 - 46 * q^17 - 9 * q^18 + 17 * q^19 - 53 * q^20 + 40 * q^21 - 15 * q^22 - 62 * q^23 - 18 * q^24 + 35 * q^25 - 29 * q^26 + 40 * q^27 + 33 * q^28 - 47 * q^29 - 14 * q^30 + q^31 - 45 * q^32 - 29 * q^33 + 9 * q^34 - 27 * q^35 + 33 * q^36 - 49 * q^37 - 52 * q^38 - 40 * q^39 - 12 * q^40 - 49 * q^41 - 9 * q^42 - 45 * q^43 - 68 * q^44 - 27 * q^45 - 36 * q^46 - 88 * q^47 + 23 * q^48 + 40 * q^49 - 32 * q^50 - 46 * q^51 - 34 * q^52 - 96 * q^53 - 9 * q^54 + 26 * q^55 - 18 * q^56 + 17 * q^57 + 12 * q^58 - 45 * q^59 - 53 * q^60 - 23 * q^61 - 15 * q^62 + 40 * q^63 + 50 * q^64 - 32 * q^65 - 15 * q^66 - 31 * q^67 - 76 * q^68 - 62 * q^69 - 14 * q^70 - 89 * q^71 - 18 * q^72 + 4 * q^73 + 10 * q^74 + 35 * q^75 + 51 * q^76 - 29 * q^77 - 29 * q^78 - 44 * q^79 - 53 * q^80 + 40 * q^81 - 15 * q^82 - 60 * q^83 + 33 * q^84 - 24 * q^85 - 9 * q^86 - 47 * q^87 - 64 * q^88 - 39 * q^89 - 14 * q^90 - 40 * q^91 - 80 * q^92 + q^93 + 51 * q^94 - 71 * q^95 - 45 * q^96 - 21 * q^97 - 9 * q^98 - 29 * q^99

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